Heterodyne Signal Research Articles

Ranging and phase measurement for LISA

The LISA phase measurement system (PMS) will provide interferometric phase readout of the primary heterodyne signal at microcycle sensitivity, ranging measurements at sub-meter accuracy and data communication at rates of several kilobits per seconds. Our investigations are focused on inter-spacecraft laser ranging and data transfer for LISA using Direct Sequence Spread Spectrum (DS/SS) modulation onto the laser links. We present the setup of an optical experimental to test the levels of performance achievable with a single laser link as well as a new hardware prototype based on FPGA (Field Programmable Gate Array) processing to perform high-accuracy phase readout of the optical signal, ranging measurements, data communication and is suitable for clock noise demodulation and digital laser-phase locking.

Characterization and compensation of the residual chirp in a Mach-Zehnder-type electro-optical intensity modulator

We utilize various techniques to characterize the residual phase modulation of a waveguide-based Mach-Zehnder electro-optical intensity modulator. A heterodyne technique is used to directly measure the phase change due to a given change in intensity, thereby determining the chirp parameter of the device. This chirp parameter is also measured by examining the ratio of sidebands for sinusoidal amplitude modulation. Finally, the frequency chirp caused by an intensity pulse on the nanosecond time scale is measured via the heterodyne signal. We show that this chirp can be largely compensated with a separate phase modulator. The various measurements of the chirp parameter are in reasonable agreement.

SIGNAL ANALYSIS OF APERTURELESS SCANNING NEAR-FIELD OPTICAL MICROSCOPY WITH SUPERLENS

Apertureless scanning near-fleld optical microscopy (A- SNOM) with a superlens is a novel nano-optical system for sub- wavelength imaging purposes. This study presents a quantitative model for analyzing the heterodyne signals obtained from an A-SNOM fltted with a superlens at various harmonics of the AFM tip vibration frequency. It is shown that the image resolution is determined not only by the tip radius, but also by the superlens transmission coe-cient in the high evanescent wave vector Kx. Moreover, the analytical results show that the images acquired from the A-SNOM/superlens system are adversely afiected by a signal contrast problem as a result of the noise generated by the tip-superlens interaction electric fleld. However, it is shown that this problem can be easily resolved using a background noise compensation method, thereby resulting in a signiflcant improvement in the signal-to-background (S/B) ratio. The feasibility of utilizing the system for maskless nanolithography applications is discussed. It is shown that the A-SNOM/superlens system in nanolithography yields a dramatic improvement in the signal intensity and S/B ratio compared to that of a conventional A-SNOM with a bare tip only.

A 2-D Heterodyne Polarimeter for the Determination of Parameters in Twisted Nematic Liquid Crystal Cells

In this paper, an experimental method for measuring the 2-D cell parameter distribution of a twisted nematic liquid crystal is presented. Based on phase-sensitive imaging polarimeter with a common-path heterodyne configuration, this study adopts an integrating-bucket method to extract 2-D phase distribution on the detected heterodyne signal for the inverse calculation of the azimuth angle (entrance director angle), twist angle, and cell gap. The advantage of the heterodyne scheme introduces high sensitivity on phase detections, and the multiple parameters could be easily extracted through the genetic algorithm. The measurement range of the azimuth angle is from 0deg to 180deg without ambiguity. By using standard 8-bit gray-level charge-coupled device, the experimental results show that the 2-D standard deviation of 0.4deg, 0.7deg, and 0.032 mum in the measurement of azimuth angle, twist angle, and cell thickness have been obtained.

Detailed design of a resonantly enhanced axion-photon regeneration experiment

A resonantly enhanced photon-regeneration experiment to search for the axion or axionlike particles is described. This experiment is a shining light through walls study, where photons traveling through a strong magnetic field are (in part) converted to axions; the axions can pass through an opaque wall and convert (in part) back to photons in a second region of strong magnetic field. The photon regeneration is enhanced by employing matched Fabry-Perot optical cavities, with one cavity within the axion generation magnet and the second within the photon-regeneration magnet. Compared to simple single-pass photon regeneration, this technique would result in a gain of $(\mathcal{F}/\ensuremath{\pi}{)}^{2}$, where $\mathcal{F}$ is the finesse of each cavity. This gain could feasibly be as high as ${10}^{10}$, corresponding to an improvement in the sensitivity to the axion-photon coupling, ${g}_{a\ensuremath{\gamma}\ensuremath{\gamma}}$, of order $(\mathcal{F}/\ensuremath{\pi}{)}^{1/2}\ensuremath{\sim}300$. This improvement would enable, for the first time, a purely laboratory experiment to probe axion-photon couplings at a level competitive with, or superior to, limits from stellar evolution or solar axion searches. This report gives a detailed discussion of the scheme for actively controlling the two Fabry-Perot cavities and the laser frequencies, and describes the heterodyne signal detection system, with limits ultimately imposed by shot noise.

Two-Frequency Paired Polarization Interferometer for Faraday Rotation Angle Detection

A highly sensitive two-frequency paired linear polarized interferometer (TPPI) for measuring the Faraday rotation angle and Verdet constant of the Bi12SiO20 (BSO) crystal in real time was set up by an amplitude-sensitive detection method. TPPI features a common-path heterodyne interferometer in conjunction with a highly correlated paired linear polarized laser beam. Then, the antisymmetry of polarized heterodyne signals is produced and Faraday rotation angle detection by a balanced detector scheme is satisfied automatically. As a result, shot-noise-limited detection of Faraday rotation angle is possible. In addition, the Faraday rotation angle detection is also insensitive to the scattering and absorption caused by the specimen because of the common-path propagation of the paired linear polarized laser beam. Experimentally, the sensitivities of Faraday rotation angle and Verdet constant measurements of the BSO crystal under the arrangement with a single pass of the laser beam in TPPI are 4.93×10-5 rad/mm and 2.6×10-7 rad/(mT·mm), respectively. This suggests that the Faraday rotation angle detection sensitivity has the potential to be on the order of 10-8 rad/mm if a Fabry–Perot cavity with a finesse of F=120 is used in TPPI.

Nonlinear response of the vacuum Rabi resonance

The exploration of the Jaynes–Cummings Hamiltonian in a circuit-QED system—where an ‘artificial atom’ made of a superconducting circuit is strongly coupled to a microwave field—provides direct evidence for nonlinearities due to quantum mechanics on the level of single atoms and photons. On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics1,2 has been reached for real atoms in optical cavities3, and for artificial atoms in circuit quantum electrodynamics4 and quantum dot systems5,6. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity, an effect known as vacuum Rabi splitting. The circuit quantum electrodynamics architecture is ideally suited for going beyond this linear-response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet and the appearance of extra peaks with the characteristic spacing of the Jaynes–Cummings ladder. These findings constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.

A Highly Phase-Sensitive Heterodyne Polariscope for the Full-Field Measurement of Twisted- Nematic Liquid Crystal

This study proposes a highly phase-sensitive imaging polariscope with a common-path heterodyne configuration for the mapping of spatially distributed cell gap of a twisted-nematic liquid crystal (TNLC). The polariscope adopts an electrooptic modulator incorporated with a quarter-wave plate to modulate the linear polarized light. By applying an integrating-bucket method, the two-dimensional (2-D) phase distribution of the detected heterodyne signal is extracted for the inverse calculation of the TNLC cell thickness. The proposing system has no need to remove or to rotate any optical elements in the measuring process and makes it possible to perform high-speed 2-D mapping. The dynamic range of retardation is around 0.7 mu m without ambiguity in the proposing method. By using a standard 8-bit gray level charged-coupled device (CCD), the experimental result shows that the standard deviation of 1.8 nm in the 2-D measurement of cell thickness has been obtained. The retardation resolution of 0.5 nm of the proposed method is also achieved and is better than that of the Stokes parameters determination method with high gray level CCD.

An analysis of heterodyne signals in apertureless scanning near-field optical microscopy

This study constructs interference-based model of the apertureless scanning near-field optical microscopy (A-SNOM) heterodyne detection signal which takes account of both the tip enhancement phenomena and the tip reflective background electric field. The analytical model not only provides a meaningful explanation of the image artifacts and errors, but also suggests methods for reducing these effects. It is shown that the detection signal obtained in the heterodyne A-SNOM method has a significantly higher signal-to-background (S/B) ratio than in the homodyne method. It is also shown that the S/B ratio increases as the wavelength of the illuminating light source is increased or the incident angle is reduced. Finally, an inspection reveals two fundamental phenomena which may potentially be exploited to obtain further significant improvements, namely (1) the modulation depth parameter has certain specific values greater than 1; and (2) the AFM tip apparatus using a ramp function.

High speed interferometric ellipsometer

A novel high speed interferometric ellipsometer (HSIE) is proposed and demonstrated. It is based on a novel differential-phase decoder which is able to convert the phase modulation into amplitude modulation in a polarized heterodyne interferometer. Not only high detection sensitivity but also fast response ability on ellipsometric parameters (EP) measurements based on amplitude-sensitive method is constructed whereas different amplitudes with respect to P and S polarized heterodyne signals in this phase to amplitude modulation conversion is discussed. The ability of HSIE was verified by testing a quarter wave plate while a real time differential-phase detection of a liquid crystal device versus applied voltage by using HSIE was demonstrated too. These results confirm that HSIE is able to characterize the optical property of specimen in terms of EP at high speed and high detection sensitivity experimentally.

Heterodyne detection with a weak local oscillator

Heterodyne detection in the limit of weak (a few photons) local oscillator and signal power levels has been largely neglected in the past, as authors almost always assumed that the noise was dominated by the shot noise from a strong local oscillator. We present the theory for heterodyne detection of diffuse and specular targets at arbitrary power levels, including the case where the local oscillator power is only a few photons per coherent integration period. The theory was tested with experimental results, and was found to show good agreement. We show how to interpret the power spectral density of the heterodyne signal and how to determine the optimal number of signal and local oscillator photons per coherent integration.

Measurement of the Field-Free Alignment of Diatomic Molecules

An apparatus was constructed to experimentally quantify the field-free alignment of diatomic molecules irradiated by strong femtosecond laser pulses. In this apparatus, both homodyne and pure heterodyne detections were realized. The alignment signal is proportional to [<cos(2)theta> - 1/3](2) for homodyne detection and (<cos(2)theta> - 1/3) for pure heterodyne detection, where theta is the polar angle between the molecular axis and the laser polarization direction. Fourier transform spectra of the homodyne signal and the pure heterodyne signal were also studied. By comparing the alignment signal and its Fourier transform spectrum with the numerical calculation of the time-dependent Schrödinger equation, we demonstrated that the pure heterodyne signal directly reproduced the alignment parameter <cos(2)theta>, and its Fourier transform spectrum provided information regarding the populations of different J states in the rotational wavepacket.

Bayesian spectrum estimation of termite signals using laser Doppler vibrometry

Laser vibrometry provides a sensitive non-invasive means of measuring substrate vibration. These measurements include landmine detection, automotive testing, production testing, aerospace, and structural testing. We employed laser vibrometry for termite detection. The vibratory signal generated by termite head banging is picked up by the laser Doppler vibrometer. In laser vibrometry, the surface motion is monitored by heterodyne laser Doppler vibrometry, and the received heterodyne signal is sampled to produce time-series data. The time-series data thus obtained is the velocity signal of the vibrating object. We consider here a statistical signal-processing approach to termite head banging data, which is based on Bayesian inference. In this approach, the quantity of interest is the frequency of vibration caused by termite head banging, while phase and quadrature amplitudes are considered nuisance parameters. We employ a single-frequency model to determine this frequency. Because of the optimal prior knowledge about the signal of interest, the frequency can be measured with much greater precision and greater noise immunity than using Fourier transform. Our results show that the Bayesian method of processing an acoustic signal exhibits excellent performance in determining the vibrational frequency.

헤테로다인 광 위상 고정 루프 연구

In this paper, the design techniques required to design heterodyned OPLL such as frequency-phase deference detector, loop filter and phase noise of semiconductor laser are presented. Through the experiments with the calculated parameters, we confirmed that the frequency-phase difference detector simply develops an error component that is proportional to the frequency-phase difference between heterodyned optical signals. The achieved frequency-phase locking range of the input laser diode frequency is around . This paper describes the details of the designed as well as experimental results.

Heterodyne interferometer for displacement measurement with amplitude quadrature and noise suppression

The high precision displacement measurement in nanoscale is crucial to many applications. We present a heterodyne interferometry with differential phase to amplitude conversion scheme for displacement measurement in nanoscale. In this approach, the differential phase introduced by the displacement is converted into the amplitudes of heterodyne signals in quadrature. Meanwhile, the heterodyne signals in phase quadrature are also achieved so that the displacement can be determined from the amplitude ratio of the quadrature signals, and the direction of displacement can be determined from the phase quadrature. Since the differential phase to quadrature amplitude conversion is achieved through the optical addition and subtraction by polarization tuning, which are based on differential detection concept. Thus the proposed method benefits from the features of differential detection with common phase noise and correlated amplitude noise rejection and that of quadrature detection with real time and wide dynamic range of phase measurement. To demonstrate the capability of proposed method in differential phase measurement, we measure the displacement drove by a commercially available PZT pusher and found close agreement between the experiment and the theory. The experimental evidence of noise suppression is also found with spectral measurements, which demonstrates the resolution of displacement measurement at 60 pm and minimum detectable differential phase of 5.6 × 10 −6 rad/ Hz over 50 kHz.

Demonstration of a laser vorticity probe in turbulent boundary layers

A laser-based probe for the nonintrusive measurement of velocity gradient and vorticity was demonstrated in turbulent boundary layers. Unlike most other optical methods, the current technique provides an estimate of the velocity gradient, without having to first measure velocity at multiple points. The measurement principle is based on the heterodyne of coherent light scattered from two adjacent particles. The beat frequency of the heterodyne is directly proportional to the velocity gradient. The probe is assembled from commercially available, inexpensive optical components. A laser Doppler velocimeter (LDV) processor is used to analyze the heterodyne signal. A component of vorticity is obtained by using two appropriately aligned velocity gradient probes. The optical probes developed were used in turbulent boundary layers to measure local, time-frozen velocity gradients partial differential u / partial differential y, partial differential v / partial differential x, and partial differential v / partial differential y, as well as the spanwise vorticity. The measurements were compared to those inferred from LDV measurements in the same facility and to data available in the literature.

In situ microfluidic flow rate measurement based on near-field heterodyne grating method

The near-field heterodyne grating (NF-HDG) method was applied to flow rate measurements in a microtube. The NF-HDG method is a newly developed optical technique based on photothermal effects. In this technique, pump light is shone on a transmission grating in front of a fluid channel and the inside liquid is heated with a pattern of the grating due to the Talbot effect. Another probe light is similarly shone on the same place as the pump light, and the diffraction by the transmission grating (reference) and the diffraction by the temporally generated thermal grating inside the fluid channel (signal) are mixed and detected (heterodyne detection). Theoretical analysis reveals that the dependence of the heterodyne signal intensity on the flow rate originates from the change in the heterodyne phase difference between the signal and reference, and the experimentally obtained calibration curves can be fitted with the theoretically predicted function. Furthermore, the optical setup was optimized based on the theoretical analysis of the Talbot effect. Flow rates of the order of nl/min were quantitatively measured, and the detection limit of the flow rate was 17 nl/min.

A Novel Heterodyne Polarimeter for the Multiple-Parameter Measurements of Twisted Nematic Liquid Crystal Cell Using a Genetic Algorithm Approach

A new method for measuring the multiple parameters of a twisted nematic liquid crystal (TNLC) by applying a genetic algorithm is presented. This paper adopts an electrooptic modulator to modulate the linear polarized light which passed through a TNLC cell in a heterodyne polarimetric setup. The intensity ratio and the phase of the detected heterodyne signal are used for the inverse calculation in the LC cell parameters by applying a genetic algorithm approach. As a result, the multiparameter measurements in the entrance director angle of TNLC, twist angle, and cell thickness are achieved. The advantage of the heterodyne polarimeter introduces high sensitivity on intensity and phase detections, and the multiple parameters could be easily extracted through the genetic algorithm. Also, the ambiguity in the angle extraction could be uniquely solved in this paper. The experimental results show that the average deviation of 0.01deg and 0.013 mum in the measurement of twist angle and cell thickness, respectively, have been obtained. The average deviation of 0.23deg in the measurement of director angle has also been achieved

The optical linear birefringence measurement using a Zeeman laser

In the paper we present a new optical system that uses a transverse Zeeman dual-frequency laser in conjunction with plane polariscope for simultaneously measuring both the principal axis angle and the retardance of the optical linearly birefringent materials. The Zeeman laser produces a standard heterodyne signal as a polarizer is set in front of a photodetector. Owing to the use of a Zeeman laser and design of optical configuration, the measurement system has the advantages of compact structure, low non-linearity, high stability, and good portability. By using the amplitudes of a reference signal and of two measuring signals, a simply derived algorithm can obtain the principal axis angle and the retardance directly and easily. The dynamic range of the principal axis angle measurement is limited in the range from 0° to 90° and that of the retardance measurement is extended to be 180° successfully. According to the measurement results, the average absolute errors of the principal axis angle and the retardance measurements for a quarter-wave plate with its principal axis angle set at 90° are determined to be 1.47° and 2.85%, respectively. The absolute error of the retardance measurement is within the uncertainty range of 5% or more for commercial quarter-wave plates.

Optical Retardation Measurement Using a Zeeman Laser

This paper presents a new optical configuration for measuring the phase retardation of optical linear birefringent materials. Phase retardation is measured by a heterodyne light source, which is generated by a Zeeman laser. The measurement system has advantages as a simple optical setup, high stability, small size, and portable owing to the configuration and the use of a Zeeman laser. Using the ratio of amplitudes from two measured heterodyne signals, a simple algorithm can obtain the phase retardation directly. Moreover, we can extend dynamic range of the phase retardation measurement to be 0 180 successfully. According to the experimental results, the average absolute error for the phase retardation of λ / 4 -wave plate sample is determined to be only 2.7 %.